Almost-Bieberbach Groups : Affine and Polynomial Structures (Lecture Notes in Mathematics)

Dekimpe, Karel

Springer Verlag（1996/12発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 259 p.
• 言語 ENG
• 商品コード 9783540618997
• DDC分類 512.55

Full Description

Starting from basic knowledge of nilpotent (Lie) groups, an algebraic theory of almost-Bieberbach groups, the fundamental groups of infra-nilmanifolds, is developed. These are a natural generalization of the well known Bieberbach groups and many results about ordinary Bieberbach groups turn out to generalize to the almost-Bieberbach groups. Moreover, using affine representations, explicit cohomology computations can be carried out, or resulting in a classification of the almost-Bieberbach groups in low dimensions. The concept of a polynomial structure, an alternative for the affine structures that sometimes fail, is introduced.

Contents

Preliminaries and notational conventions.- Infra-nilmanifolds and Almost-Bieberbach groups.- Algebraic characterizations of almost-crystallographic groups.- Canonical type representations.- The Cohomology of virtually nilpotent groups.- Infra-nilmanifolds and their topological invariants.- Classification survey.